Look at a part like thishttp://www.ti.com/lit/ds/symlink/l293d.pdfIt uses transistors to basically switch the motor leads from +supply/gnd for current flow in one direction, to gnd/+supply for current flow the other direction to make the motor spin the other direction.Depending on how big your motor is, what voltage/current is required, you may be able to use this part, or find a beefier part, or use discrete transistors with a chip like this to drive/control the transistors. You may be able to use an existing motor shield for this.

What will the source for your HIGH/LOW signal? Reading that from a digital pin is usually the easist part of the project, such as from a mechanical switch.

So you want forward/stop/reverse control based on inputs from several transducers. Yes, that would require a micro-controller and an H-bridge, (or a transistor and a relay). But a simple H-bridge can be constructed from four jelly-bean transistors and is quite a simple circuit.

Would you have a link for me to make the circuit?

Or, would I just use the Arduino and the H-bridge ( http://www.ti.com/lit/ds/symlink/l293d.pdf )??

I am new to this, so no0b based information would be easier to understand.